As druids can't use crossbows, could the Spider wildshapes be modified to let them shoot silk strands to work in much the same way as grapple guns?
Some wildshape forms definitely should give climbing bonuses. Which would likely be easier to implement than giving them a special climb ability.
I know of at least one wild shape that already gives a large bonus to basic tumble/climb checks. At least that's how it was in EFU:M
if wild shape forms can give various EFUSS climb bonuses, this would be sufficient. Not all druids take tumble.